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Question

If A is a square matrix of order 3, then |(AAT)105| is equal to

A
105|A|
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B
105|A|2
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C
105
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D
none of these
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Solution

The correct option is D none of these
(AAT)105=(ATA)105

=ATA105
=(ATA)T105 ( determinant of matrix and its transpose is equal)
=AAT105
AAT105=AAT105=0( determinant of skew-symmetric matrix of odd order is 0.)

(AAT)105=0
Hence, option 'D' is correct.

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